Research designs and statistical software solutions

The following overview collects information about available software solutions for each design. Suggested literature in the 'comments' column mainly refers to methodological papers. For examples of the respective designs, please refer to Designs.

Design

Software

Comment

Unidirectional/

Ego-centered

Only a single individual is being analyzed with regard to his or her social relationships (non-reciprocal).

When collecting ego-centered network data, participants are typically asked to list all network partners who belong to a certain category. For example, researchers may request participants to list all people with whom they interact at least once a weak, or all people whom they consider as friends. These network partners are then rated on one or more characteristics.

To prepare corresponding analyses, the raw data file should be set up to correspond to its multilevel structure, with each participant contributing as many cases (“lines” in most statistical programs) as the number of network partners. The columns of the resulting data set then represent participants' ratings on various dimensions.

Multivariate pseudo-dyadic analyses using multilevel modeling

Retaining the original data structure, analyses must be conducted using multilevel software, with ratings of network partners nested within participants. When such a structure is specified, intercepts (means of the dependent variable) and slopes (associations between independent and dependent variables) can be estimated. These estimates are weighted according to the number of data points that each individual rater contributes. Thus, estimates are more heavily influenced by participants with large ego-centered networks.

A main advantage of multilevel modeling is that these estimates can be allowed to vary across participants. For example, some people may show a strong covariance between perceived physical attractiveness and liking in their ratings of network partners, whereas other perceivers may rate these dimensions relatively independently. Multilevel modelling allows the researcher to predict such differences using between-person variables (e.g., gender, personality).

Special attention needs to be given to the centering of the variables: Imagine that a researcher would use multilevel modeling to estimate how the amount of rated conflict is associated with the amount of rated closeness within participants' individual networks. In this case, he/she must take into account that the resulting slope estimate mixes both within- and between-person variance if the data are not centered within participants/raters. Such centering of the data may also be regarded as a relatively crude way to eliminate the perceiver effect (bias), though the resulting estimates would still confound target and relationship variance.

Aggregation of network characteristics across raters

Another approach that eliminates the multilevel structure of the data is to aggregate all ratings across individual raters. Taking the above example, the average degree of conflict and closeness that is reported by every participant may be computed. These aggregated scores can then be used as variables in conventional statistical analyses. For example, one could correlate personality variables with average aggregated network parameters or use them as dependent or independent variables in a multiple regression. It should be noted, however, that the corresponding aggregates confound perceiver and target effects. For example, it is not possible to say whether participants who rate their network partners as highly supportive do so because they tend to judge other people favorably or because they have relationships with genuinely supportive others.

Half-Block-Design

Conventional Software

Calculation of variance components

Variance components can be estimated with a multi-level model (aka hierarchical linear model or mixed effects model) with two random factors (one for actor variance, one for partner variance). In case of multiple groups, group has to be specified as third random factor. In R, this can be done with the lme4-package by calculating an intercept-only model with random effects with following syntax. For more details and syntax on how to analyse half block designs with SPSS or SAS see Kenny (2007).

Calculation of actor, partner, and relationship effects

Actor and partner effects are row- and column means (minus grand mean), and the relationship effect is each cell minus its row-, column-, and grand mean (see Kenny, 1994; formulae).

Single partner

Two members of an existing dyad are analyzed (reciprocal).

Distinguishable

Dyads

Conventional Software

MLM and SEM Software

For dyadic data of both distinguishable and indistinguishable dyads the estimation of actor-partner-interdependence models (APIM) is the most advanced and convenient statistical method.

In APIM analysis, actor and partner effects are profoundly different from actor and partner effects in SRM analyses, and therefore have the preposition “dyadic”. Dyadic actor effects refer to the effect of one’s own score on X on one’s own score on Y, whereas dyadic partner effects refer to effects of one’s own score on X on the partner’s score on Y.

For analyzing dyadic data, most conventional statistical software (such as SPSS, SAS) is applicable, even though estimation of APIMs is conducted most frequently in MLM and SEM (using AMOS, Mplus, HLM, etc.). Take note: MLM and SEM analyses require different data structures. Using MLM, the data set has to be in a pairwise structure (also called double-entry structure). Thus, there is a record for scores of each individual combined with the scores of the dyadic partner. In contrast, for an application of SEM a dyadic data structure is required with one record for each dyad only.

(Figure of APIM-Model)

Dyadic actor effects illustrate intrapersonal effects and dyadic partner effects illustrate interpersonal effects. In addition, the correlation between X1 and X2 represent a compositional effect and the correlation between E1 and E2 represents the nonindependence not explained by the APIM. APIM analyses may also incorporate several predictor variables (i.e., moderator and mediator variables) or interaction effects. Dyadic analyses are conducted either if outcome variables of the dyadic partners are dependent or if researchers are interested in dyadic actor and partner effects. Since dyadic analyses do not provide the possibility to differentiate between SRM effects, estimates confound actor, partner and relationship variance.

In distinguishable dyads there are two potential dyadic actor effects, one for each dyad member, and two potential dyadic partner effects, one from person 1 on person 2 and vice versa. For example researcher interested in parent-child relationships are able to directly compare effects that parents have on their children and vice versa.

Indistinguishable Dyads

Conventional Software

MLM and SEM Software

In indistinguishable dyads the two potential dyadic actor effects and the two potential dyadic partner effects are both required to be equal. Thus the actor effect of person 1 (statistically) equals the actor effect of person 2. The same is true for the partner effects. Hence in indistinguishable dyads actor and partner effects generalize across both dyadic partners.

For an introduction and further literature to APIM analyses see also David Kenny’s homepage, Kenny, Kashy & Cook (2006) or Gonzalez & Griffin (2002).

Calculation of variance components and their interrelations

BLOCKO

BLOCKO (Kenny, 1995) is a tailored software to analyse block designs (half block, asymmetric and symmetric full block designs). The program partitions variance into actor, partner, and relationship components, and outputs the relative variance of each component. If latent constructs are measured with multiple indicators, the variances of these constructs are partitioned. Furthermore, various correlations among the different types of SRM effects, between SRM effects of separate variables (bivariate SRM analysis), and between SRM effects and individual-difference variables are also computed. Multiple groups are allowed, but there has to be the same number of persons in each group.

Significance tests are based on between-groups t-tests, i.e. SRM parameters are computed separately for each of the groups and subsequently the distribution of these parameters is tested against zero. Whereas the between-group t-test works well when the data consist of many full block groups, this strategy may not be used when you have only a few or even only a single group. In this case, BLOCKO tests the parameters for significance by using the jackknife method, which is, however, rather conservative and is not recommended (Kenny, Kashy, & Cook, 2006, p. 213; Lashley & Bond, 1997).

Conventional software

Variance components in a asymmetric block design can be estimated with a multi-level model (e.g., by using R, SPSS, SAS). For an introduction on how to analyse asymmetric full-block designs with SPSS or SAS see Kenny (2007).
A symmetric block design cannot analyzed as easily as a asymmetric block design with conventional software, although it may be analyzed by treating it as a round robin design with missing data (see below).

Calculation of actor, partner, and relationship effects

As in half-block designs, actor and partner effects simply are row- and column means (minus grand mean), and the relationship effect is each cell minus its row-, column-, and grand mean (formulae; Kenny, 1994) (i.e. the actor effect is calculated in Block A and the partner effect in Block B).

Further analyses with SRM effects

Correlations between actor and partner effects and individual-difference variables (e.g., dispositions) can be computed with any statistic software (e.g., R, SPSS, SAS). In case that you have different full block groups, the effect of groups has to be partialed out (see Kenny, Kashy, & Cook, 2006, p. 209). Associations between relationship effects and dyadic variables (e.g., similarity in dispositions) can be estimated with a subsequent APIM analysis (see Kenny et al., p. 210).

Calculation of variance components and their interrelations

SOREMO

The computer program SOREMO (Kenny, 1998) is a very powerful software for the analysis of multivariate Round-Robin data using a Social Relations Model (SRM) approach (Kenny, 1994). The program partitions variance into actor, partner, and relationship components, and outputs the relative variance of each component. If latent constructs are measured with multiple indicators, the variances of these constructs are partitioned. Furthermore, various correlations among the different types of SRM effects, between SRM effects of separate variables (bivariate SRM analysis), and between SRM effects and individual dispositions are also computed. Actor, partner, and relationship effects can be read out for further analyses (see below).

SOREMO is virtually unrestricted regarding to the number of groups, whereas each group is restricted to consist of no more than 25 participants. Missing data are not allowed. Significance tests are based on between-groups t-tests, i.e. SRM parameters are computed separately for each of the groups and subsequently the distribution of these parameters is tested against zero. Whereas the between-group t-test works well when the data consist of many Round-Robin groups, this strategy may not be used when you have only a few or even only a single Round-Robin group. In this case, SOREMO tests the parameters for significance by using the jackknife method, which is, however, rather conservative and is not recommended (Kenny, Kashy, & Cook, 2006, p. 213; Lashley & Bond, 1997). Thus, SOREMO is particularly well suited for analyzing datasets consisting of several Round-Robin groups, whereas it is less powerful in case of one single Round-Robin group and even unsuited for analyzing a Round-Robin group consisting of more than 25 participants.

TripleR

In case that you want to analyze one large Round-Robin group, we recommend using TripleR, a package for the statistic software R. Given this kind of data, TripleR has two advantages over SOREMO: First, TripleR is not restricted regarding to the number of participants. Second, TripleR uses within-group t-tests (Bond & Lashley, 2006), which were shown to be superior to the jackknife method (Lashley & Bond, 1997).

Similar to SOREMO, TripleR allows to partition variance into actor, partner, and relationship components, and outputs the relative variance of each component. If latent constructs are measured with two indicators, the variances of these constructs are partitioned. Furthermore, various correlations among the different types of SRM effects, and between SRM effects of separate variables (bivariate SRM analysis) are also computed. Actor, partner, and relationship effects can be read out for further analyses (see below). Although at the present TripleR may only be used for analyzing data based on a single Round-Robin group with no missings, future versions of TripleR will be able to handle multiple groups and missing data.

Conventional Statistic Software

It is also possible to use conventional statistic software (such as SPSS, SAS, and structural equation software) to analyze Round-Robin data based either on multi-level modeling oder structural equation modeling (see Kenny, 2007). With this software it is possible to partition variance into actor, partner, and relationship components and to compute the various correlations among the different types of SRM effects (however, some of these analyses assume the actor-partner covariance be zero). At the present, Kenny (2007) only considers the case of univariate Round-Robin analyses. Thus, in particular for multivariate Round-Robin analyses, we would recommend using the above described specialized software.

Calculation of actor, partner, and relationship effects

Formulae for computing SRM effects for Round-Robin data are described in Kenny (1994). These effects cannot easily be computed with conventional software, but can be read out for further analyses with SOREMO and TripleR.

Further analyses with SRM effects

Correlations between actor and partner effects and individual-difference variables (e.g., dispositions) can be computed with any statistic software (e.g., R, SPSS, SAS). In case that you have different Round-Robin groups, the effect of groups has to be partialed out (see Kenny, Kashy, & Cook, 2006, p. 209). Associations between relationship effects and dyadic variables (e.g., similarity in dispositions) can be computed with a subsequent APIM analysis (see Kenny et al., p. 210).

SIENA is a program developed by Tom Snijders to analyze social network data. As described under Designs, such analyses require dichotomous data in the form of dyadic nominations (e.g., one person selecting another person as a friend). If you are new to social network analysis, setting up and analyzing the data using SIENA is a rather difficult enterprise that likely requires instruction by experienced users (e.g., by following a workshop or spending some time at a lab in which this software is frequently used). For those bold users who want to learn the program autodidactically, a detailed manual (SIENA 3.2) is available on the SIENA homepage.

An exciting new development in the social network analysis community is the work on a RSiena (SIENA 4), which uses the the open source R statistical platform. A detailed manual is available on the SIENA homepage.